Yes, the Newton used "soups" (essentially simple databases) for data storage instead of a filesystem, but I never had the impression that this was because of flash memory. I believe it had more to do with reducing the size and complexity of applications by having long-term storage use the same data format as heap storage. On the Newton, you didn't have to "format" data when storing it to a soup or "parse" it when reading it. As far as applications were concerned, soups stored associative arrays just like the rest of NewtonScript did.

Soups were stored in a flat namespace rather than a hierarchical one, largely because the Newton was designed as a single-user device where each application worked with a single data set. The flat namespace and standard data format encouraged data sharing between applications: it was trivially easy to lookup a name in the address book, for example.

The original Palm OS also used "databases" in a flat namespace rather than a filesystem, and for largely the same reasons. Again, I don't think that flash memory had much to do with it. In fact, when Palm OS started supporting external flash memory cards, they used the FAT filesystem (for compatibility with digital cameras and desktop card readers) rather than porting their existing database format.